Pseudogap in one dimension

Two decades ago, Sadovskii found an exact solution for a model describing a pseudogap in electron energy spectrum (introduced by Lee, Rice, and Anderson). The discovery of a pseudogap in high-Tc superconductors has revived interest in his exact solution. I review the model with the emphasis on physical content, point out an error in the original Sadovskii solution, and explain which problem he actually solved. A recent incorporation of Sadovskii's ideas into a description of ``hot spots'' on the Fermi surface in cuprate superconductors (Schmalian, Pines, and Stojkovi {c} \'{c}{}) is briefly discussed.